| With the development of 3D acquisition technologies and computational power, conformal geometry plays increasingly important role in engineering fields. Conformal geometry has deep roots in pure mathematics, combining complex analysis, Riemann surface theory, differential geometry, and algebraic topology. In recent years, theory of discrete conformal geometry has been developed. They have been extensively applied in many practical fields.;Surface remeshing plays a significant role in computer graphics and visualization. Numerous surface remeshing methods have been developed to produce high quality meshes. Generally, the mesh quality is improved in terms of vertex sampling, regularity, triangle size and triangle shape. Many of such surface remeshing methods are based on Delaunay refinement. We present a surface remeshing method based on uniformization theorem using dynamic discrete Yamabe flow and Delaunay refinement, which performs Delaunay refinement on the conformal uniformization domain.;Surface based shape analysis plays an important role in computer vision and medical imaging. We present a Wasserstein distance method based on optimal mass transport (OMT) theory for shape classification of brains hippocampus in epilepsy, and demonstrate the potential of our method on the discriminative analysis of hippocampal shape in epilepsy.;Surface registration plays a fundamental role in computer vision too. It is important to obtain a unique bijective registration for surfaces with landmarks constraints. We present a surface registration method based on optimal mass transport map (OMT-Map) and Teichmuller map (T-Map). |
